Calculate the Area of a Deltoid with Height 7 and Width 4 Units

Deltoid Area with Diagonal Measurements

Look at the deltoid in the figure:

777444

What is its area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the area of the kite
00:03 We'll use the formula to calculate the kite's area
00:08 (diagonal times diagonal) divided by 2
00:13 Let's solve to find the area
00:19 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the deltoid in the figure:

777444

What is its area?

2

Step-by-step solution

Let's begin by reminding ourselves of the formula for the area of a kite

Diagonal1×Diagonal22 \frac{Diagonal1\times Diagonal2}{2}

Both these values are given to us in the figure thus we can insert them directly into the formula:

(4*7)/2

28/2

14

3

Final Answer

14

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of kite/deltoid equals diagonal₁ × diagonal₂ ÷ 2
  • Technique: Multiply perpendicular diagonals: 4 × 7 = 28, then divide
  • Check: Area must be less than rectangle with same dimensions: 14 < 28 ✓

Common Mistakes

Avoid these frequent errors
  • Using length × width like a rectangle
    Don't calculate 4 × 7 = 28 as final answer! A deltoid is not a rectangle, so base × height doesn't work. Always use the diagonal formula: d1×d22 \frac{d_1 \times d_2}{2} = 4×72 \frac{4 \times 7}{2} = 14.

Practice Quiz

Test your knowledge with interactive questions

Indicate the correct answer

The next quadrilateral is:

AAABBBCCCDDD

FAQ

Everything you need to know about this question

What's the difference between a deltoid and a kite?

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A deltoid is just another name for a kite! Both are quadrilaterals with two pairs of adjacent sides that are equal in length.

Why do we divide by 2 in the formula?

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The diagonals of a kite split it into 4 triangles. The formula d1×d22 \frac{d_1 \times d_2}{2} calculates the total area by finding half the area of the rectangle formed by the diagonals.

How do I know which measurements are the diagonals?

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Diagonals are the perpendicular lines that cross inside the shape, connecting opposite vertices. In this problem, the vertical line (height 7) and horizontal line (width 4) are the diagonals.

Can I use this formula for any quadrilateral?

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No! This diagonal formula only works for kites and rhombuses where the diagonals are perpendicular. For other quadrilaterals, you need different area formulas.

What if the diagonals aren't perpendicular?

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Then you can't use this simple formula! The d1×d22 \frac{d_1 \times d_2}{2} formula specifically requires perpendicular diagonals, which is a special property of kites.

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